Convergence theorems of monotone $(\alpha, \beta)$-nonexpansive mappings for normal-S iteration in ordered Banach spaces with convergence analysis

Authors

  • K. Muangchoo-in King Mongkut's University of Technology Thonburi (KMUTT). Bangkok, Thailand.
  • P. Kumam KMUTTFixed Point Research Laboratory, KMUTT-Fixed Point Theory and Applications Research Group, SCL 802 Fixed Point Laboratory, Department of Mathematics, Faculty of Science, KMUTT, Bangkok 10140, Thailand http://orcid.org/0000-0002-5463-4581
  • J- Yao Research Center for Interneural Computing, China Medical University Hospital China Medical University, Taichung, 40402, Taiwan
  • C- Wen Center for Fundamental Science, and Research Center for Nonlinear Analysis and Optimization, Kaohsiung Medical University, 100, Shih-Chuan 1st Road, Kaohsiung, 80708, Taiwan

Abstract

In this work, we prove some theorems of existence of fixed points for a monotone (α, β)-nonexpansive mapping in a uniformly convex ordered Banach space. Also, we prove some weak and strong convergence theorems of normal-S iteration under some control condition. Finally, we give two numerical examples to illustrate the main result in this paper.

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Published

2020-01-10

How to Cite

Muangchoo-in, K., Kumam, P., Yao, J.-., & Wen, C.-. (2020). Convergence theorems of monotone $(\alpha, \beta)$-nonexpansive mappings for normal-S iteration in ordered Banach spaces with convergence analysis. Journal of Nonlinear Analysis and Optimization: Theory & Applications, 11(1), 73-86. Retrieved from http://www.math.sci.nu.ac.th/ojs302/index.php/jnao/article/view/566

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Section

Research Article

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